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Chapter 4: Q2. (page 143)

Place the statements in an appropriate order for a proof.

Given: KL¯⊥LA¯;KJ¯⊥JA;¯AK→ bisects ∠LAJ.

Prove:LK¯≅JK¯

(a)KL¯⊥LA¯;KJ¯⊥JA¯

(b)role="math" localid="1648877403238" ∠1≅∠2

(c)AK→ bisects∠LAJ

(d) m∠L=90;m∠J=90

(e)LK¯≅JK¯

(f)∠L≅∠J

(g)ΔLKA≅ΔJKA

(h)KA¯≅KA¯

Short Answer

Expert verified

The statements in an appropriate order for a proof is:

(a),(d),(f),(c),(b),(h),(g),(e).

Step by step solution

01

­- Observe the gien diagram.

The given diagram is:

02

- Description of step.

It is given that KL¯⊥LA¯; KJ¯⊥JA¯.

As, KL¯⊥LA¯, therefore m∠L=90.

As, KJ¯⊥JA¯, therefore m∠J=90.

As, m∠L=90and m∠J=90, therefore ∠L≅∠J.

It is also given that AK→bisects ∠LAJ.

As, AK→bisects ∠LAJ, therefore ∠1≅∠2.

By using the reflexive property, KA¯≅KA¯.

In the triangles ΔLKAand ΔJKA, it can be noticed that:

∠L≅∠J,∠1≅∠2and KA¯≅KA¯.

Therefore, by using AAS postulate, it can be said that ΔLKA≅ΔJKA.

Therefore, by using the corresponding parts of congruent triangles it can be said that LK¯≅JK¯.

03

- Description of step.

The statements in an appropriate order for a proof is:

(a),(d),(f),(c),(b),(h),(g),(e).

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Most popular questions from this chapter

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to ΔABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

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